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Abstract We definelazinessto describe a large suppression of variational parameter updates for neural networks, classical or quantum. In the quantum case, the suppression is exponential in the number of qubits for randomized variational quantum circuits. We discuss the difference between laziness andbarren plateauin quantum machine learning created by quantum physicists in McCleanet al(2018Nat. Commun.91–6) for the flatness of the loss function landscape during gradient descent. We address a novel theoretical understanding of those two phenomena in light of the theory of neural tangent kernels. For noiseless quantum circuits, without the measurement noise, the loss function landscape is complicated in the overparametrized regime with a large number of trainable variational angles. Instead, around a random starting point in optimization, there are large numbers of local minima that are good enough and could minimize the mean square loss function, where we still have quantum laziness, but we do not have barren plateaus. However, the complicated landscape is not visible within a limited number of iterations, and low precision in quantum control and quantum sensing. Moreover, we look at the effect of noises during optimization by assuming intuitive noise models, and show that variational quantum algorithms are noise-resilient in the overparametrization regime. Our work precisely reformulates the quantum barren plateau statement towards a precision statement and justifies the statement in certain noise models, injects new hope toward near-term variational quantum algorithms, and provides theoretical connections toward classical machine learning. Our paper provides conceptual perspectives about quantum barren plateaus, together with discussions about the gradient descent dynamics in Liuet al(2023Phys. Rev. Lett.130150601).
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An unusual potassium conductance protects Caenorhabditis elegans pharyngeal muscle rhythms against environmental noise
The nematodeCaenorhabditis elegansfeeds by rhythmic contraction and relaxation of a neuromuscular organ called the pharynx, which draws in and filters water and bacterial food. This behavior is driven by myogenic plateau potentials, long-lasting depolarizations of the pharyngeal muscle, which are timed by neuronal input from a dedicated pharyngeal nervous system. While the timing of these plateaus’ initiation has received significant attention, their mechanisms of termination remain incompletely understood. In particular, it is unclear how plateaus resist early termination by hyperpolarizing current noise. Here, we present a computational model of pharyngeal plateaus against a noisy background. We propose that an unusual, rapidly inactivating potassium conductance confers exceptional noise robustness on the system. We further investigate the possibility that a similar mechanism in other systems permits switching between plateau and spiking behavior under noisy conditions.
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- Award ID(s):
- 2426394
- PAR ID:
- 10639277
- Publisher / Repository:
- National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 122
- Issue:
- 14
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1073/pnas.2422709122
